On the connection between discontinuous step-like and smooth kink-type classical solutions in quantum field theory

Sveshnikov, K. A.; Silaev, P. K.

doi:10.1007/bf02070673

Cited by 4 publications

(4 citation statements)

References 31 publications

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“…Generalizing to fermion problem (1.7) is trivial. We introduce the functional 10) whereφ(ξ) = φ * (ξ * ) is also an analytic function in the strip |Im ξ| < if φ(ξ) is analytic and also has the same asymptotic properties. Furthermore, we also require that after the passage to the momentum representation, the functional K[φ] have the form 11) whereφ(k) is the Fourier transform of φ(ξ), and that it take finite values for the admissible functions φ(ξ).…”

Section: Introductionmentioning

confidence: 99%

“…Here, as in [7], we proceed from the analysis in [10] in the framework of the problem of covariantly quantizing the field in Lorentz bases and consider only those φ(ξ) and χ(ξ) that have an analytic continuation to the strip |Im ξ| < . In this case, we have…”

Section: Introductionmentioning

confidence: 99%

“…( 1.9) Furthermore, φ(ξ) and χ(ξ) as wave functions of bound states must satisfy the condition of square integrability on the real axis, and the results in [10] imply an additional condition in this case: these functions must take zero limit values in the strip |Im ξ| < as |ξ| → ∞. The analyticity condition for the solutions of Eqs.…”

Section: Introductionmentioning

confidence: 99%

“…The analyticity condition for φ(ξ) and χ(ξ) in the strip |Im ξ| < can be given a rather clear physical interpretation [7], [10]. For brevity, we confine ourself here to only the boson case.…”

Section: Introductionmentioning

confidence: 99%

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Quasi-exact solution of the problem of relativistic bound states in the (1+1)-dimensional case

Sveshnikov

Silaev

2006

Theor Math Phys

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We investigate the problem of bound states for bosons and fermions in the framework of the relativistic configurational representation with the kinetic part of the Hamiltonian containing purely imaginary finite shift operators e ±i d/dx instead of differential operators. For local (quasi)potentials of the type of a rectangular potential well in the (1+1)-dimensional case, we elaborate effective methods for solving the problem analytically that allow finding the spectrum and investigating the properties of wave functions in a wide parameter range. We show that the properties of these relativistic bound states differ essentially from those of the corresponding solutions of the Schrödinger and Dirac equations in a static external potential of the same form in a number of fundamental aspects both at the level of wave functions and of the energy spectrum structure. In particular, competition between and the potential parameters arises, as a result of which these distinctions are retained at low-lying levels in a sufficiently deep potential well for 1 and the boson and fermion energy spectra become identical.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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